1. Lecture Slides Elementary Statistics Eleventh Edition
and the Triola Statistics Series
by Mario F. Triola
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2. Chapter 2 Summarizing and Graphing Data
2-1 Review and Preview
2-2 Frequency Distributions
2-3 Histograms
2-4 Statistical Graphics
2-5 Critical Thinking: Bad Graphs
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3. Section 2-1 Review and Preview
In the last chapter we discussed collecting and analyzing data sets.
Data sets are usually very large and nobody wants to look at tables of numbers…
=> Data has to be represented graphically.
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4. Frequency Distributions
Section 2-2
Frequency Distributions
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5. Definition Frequency Distribution (or Frequency Table)
shows how a data set is partitioned among all of several categories (or classes) by listing all of the categories along with the number of data values in each of the categories.
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6. Pulse Rates of Females and Males
Original Data
Simple random samples of 40 females and 40 males.
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7. Frequency Distribution Pulse Rates of Females
The frequency for a particular class is the number of original values that fall into that class.
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8. Frequency Distributions
Definitions
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9. Lower Class Limits Lower Class Limits
are the smallest numbers that can actually belong to different classes
Lower Class
Limits
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10. Upper Class Limits Upper Class Limits
are the largest numbers that can actually belong to different classes
Upper Class
Limits
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11. Class Boundaries Class Boundaries
are the numbers used to separate classes, but without the gaps created by class limits
59.5
69.5
79.5
89.5
99.5
109.5
119.5
129.5
Class
Boundaries
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12. Class Midpoints Class Midpoints
are the values in the middle of the classes and can be found by adding the lower class limit to the upper class
limit and dividing the sum by two
64.5
74.5
84.5
94.5
104.5
114.5
124.5
Class
Midpoints
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13. Class Width Class Width
is the difference between two consecutive lower class limits or two consecutive lower class boundaries
Class
Width 10
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14. Relative Frequency Distribution
includes the same class limits as a frequency distribution, but the frequency of a class is replaced with a relative frequencies (a proportion) or a percentage frequency ( a percent)
relative frequency =
class frequency
sum of all frequencies
percentage
frequency
class frequency
sum of all frequencies
 100% =
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15. Relative Frequency Distribution*
Sum of relative frequencies
should total to 1 or 100%
Total Frequency = 40
* 12/40  100 = 30%
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16. Cumulative Frequency Distribution Cumulative Frequencies
= sum of frequencies for that class and all previous classes
Cumulative Frequencies
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17. Data->Data Analysis->Histogram
1st install Data Analysis Toolpack (Excel Options, Data Analysis, press Go)
File FHEALTH Data->Data Analysis->Histogram
Select data
Data->Data Analysis->Histogram
To install Data Analysis toolpack go to
Excel Options and choose Add-Ins
Do not forget to click on GO
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18. Critical Thinking Interpreting Frequency Distributions
In later chapters, there will be frequent reference to data with a normal distribution.
One key characteristic of a normal distribution is that it has a “bell” shape.
The frequencies start low, then increase to one or two high frequencies, then decrease to a low frequency.
The distribution is approximately symmetric, with frequencies preceding the maximum being roughly a mirror image of those that follow the maximum.
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19. Public and Private 2 and 4 year colleges.
Table 2.5, p 50 IQ scores of 1000 adults – looks normal
Graphs above are for quantitative data, but they can also be used for qualitative data.
Ex 6, p 52, Table 2.9 Distribution of undergraduate college student enrollment among
Public and Private 2 and 4 year colleges.
My example: Degree of Agreement
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21. Section 2-3 Histograms Copyright © 2010 Pearson Education
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22. Histogram Basically a graphic version of a frequency distribution.
STATDISK
Data->Hystogram
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23. Relative Frequency Histogram
Has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies – better for comparison with other histograms.
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25. Critical Thinking Interpreting Histograms
Objective is not to construct a histogram (computer job), but rather to understand something about the data (center, variation, distribution, outliers, etc…)
For example, when graphed, a normal distribution has a “bell” shape. Characteristic of the bell shape are:
(1) The frequencies increase to a maximum, and then decrease, and
(2) symmetry, with the left half of the graph roughly a mirror image of the right half.
The histogram on the next slide illustrates this.
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26. Statdisk-generated histogram of 1000 IQ’s Table 2.5 p 50
When graphed, a normal distribution has a “bell” shape. Characteristic of the bell shape are
The frequencies increase to a maximum, and then decrease
symmetry, with the left half of the graph roughly a mirror image of the right half.
Statdisk-generated histogram of 1000 IQ’s Table 2.5 p 50
Statdisk-generated histogram of Datasets -> Female
Health Exam file, 2nd column - height
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27. Section 2-4 Statistical Graphics
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28. Frequency Polygon
Uses line segments connected to points directly above class midpoint values
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29. Relative Frequency Polygon
Uses relative frequencies (proportions or percentages) for the vertical scale.
It is crucial to use relative frequencies when comparing data sets
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30. Ogive A line graph that depicts cumulative frequencies
- Useful for determining the number of values below some particular value
class boundaries
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31. Bar Graph
Uses bars of equal width to show frequencies of categories of qualitative data.
Vertical scale represents frequencies or relative frequencies.
Horizontal scale identifies the different categories of qualitative data.
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32. Multiple Bar Graph
A multiple bar graph has two or more sets of bars, and is used to compare two or more data sets.
Median Income of Males and Females
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33. Scatter Plot (or Scatter Diagram)
A plot of paired (x,y) data with a horizontal x-axis and a vertical y-axis.
Used to determine whether there is a relationship between the two variables
Temperature vs number of
cricket chirps per minute.
There appears to be a
relationship.
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34. More scatter plot examples:
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35. Using StatDisk height(inches) vs weight (lbs)
for Female Health Exam data
Excel
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37. Time-Series Graph
Data that have been collected at different points in time: time-series data
Example: Dow Jones Industrial Average vs Time:
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38. More examples of time series
We describe time series by looking for an overall pattern and for striking deviations from that pattern. In a time series:
A trend is a rise or fall that persists over time, despite small irregularities.
A pattern that repeats itself at regular intervals of time is called seasonal variation.
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39. Retail price of fresh oranges over time
Time is on the horizontal, x axis.
The variable of interest—here “retail price of fresh oranges”— goes on the vertical, y axis.
This time plot shows a regular pattern of yearly variations.
These are seasonal variations in fresh orange pricing most likely due to similar seasonal variations in the production of fresh oranges.
There is also an overall upward trend in pricing over time.
It could simply be reflecting inflation trends or a more fundamental change in this industry.
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40. Critical Thinking: Bad Graphs
Section 2-5
Critical Thinking: Bad Graphs
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41. Nonzero Axis
Are misleading because one or both of the axes begin at some value other than zero, so that differences are exaggerated.
Ex: Left – bar graph of CNN poll regarding the case of Terry Schiavo.
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42. Another example of graph not starting at 0:
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43. Pictographs -- are drawings of objects.
Three-dimensional objects - money bags, stacks of coins, army tanks (for army expenditures), people (for population sizes), barrels (for oil production), and houses (for home construction) are commonly used to depict data.
These drawings can create false impressions that distort the data.
If you double each side of a square, the area does not merely double; it increases by a factor of four;
If you double each side of a cube, the volume does not merely double; it increases by a factor of eight.
Pictographs using areas and volumes can therefore be very misleading.
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44. Pictographs
Part (b) is designed to exaggerate the difference by increasing each dimension in proportion to the actual amounts of oil consumption.
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45. Annual Incomes of Groups with Different Education Levels
-- not misleading because the bars have same width. But somewhat too busy.
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46. Annual Incomes of Groups with Different Education Levels
Misleading. Depicts one-dimensional data with three-dimensional boxes. Last box is 64 times as large as first box, but income is only 4 times as large.
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47. Annual Incomes of Groups with Different Education Levels
Fair, objective, no distracting features.
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48. What is wrong with these graphs?
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